Classical and Quantum Aspects of BPS Black Holes in N=2, D=4 Heterotic String Compactifications

TL;DR

<3-5 sentence high-level summary>This paper investigates how classical and quantum aspects of $D=4$, $N=2$ BPS black holes in heterotic string compactifications behave under dynamical relaxation of moduli fields, using the STU model as a concrete setting. It develops a unified framework based on rigid and local $N=2$ special geometry to derive a simpler, general derivation of the Ferrara-Kallosh extremized mass and entropy and extends the concept of moduli relaxation to backgrounds with BPS solitons and black holes. The author proves perturbative non-renormalization theorems grounded in target-space duality, showing that BPS mass and entropy retain their classical form when expressed in renormalized string loop-counting parameters and moduli, and derives leading non-perturbative corrections in the large-$T_2$ limit. The work further discusses how these results map under string-string dualities to Type I and Type IIA Calabi-Yau black holes, providing a robust framework for understanding BPS black holes across weak and strong coupling regimes and their microscopic-macroscopic consistency.</3-5 sentence high-level summary>

Abstract

We study classical and quantum aspects of D=4, N=2 BPS black holes for T_2 compactification of D=6, N=1 heterotic string vacua. We extend dynamical relaxation phenomena of moduli fields to background consisting of a BPS soliton or a black hole and provide a simpler but more general derivation of the Ferrara-Kallosh's extremized black hole mass and entropy. We study quantum effects to the BPS black hole mass spectra and to their dynamical relaxation. We show that, despite non-renormalizability of string effective supergravity, quantum effect modifies BPS mass spectra only through coupling constant and moduli field renormalizations. Based on target-space duality, we establish a perturbative non-renormalization theorem and obatin exact BPS black hole mass and entropy in terms of renormalized string loop-counting parameter and renormalized moduli fields. We show that similar conclusion holds, in the large T_2 limit, for leading non- perturbative correction. We finally discuss implications to type-I and type-IIA Calabi -Yau black holes.